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Warranty Data Analysis Example
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This example validates the results of a warranty data analysis in a Weibull++ warranty folio.
Reference Case
The data set is from Example 11.2 on page 453 in the book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.
Data
A Nevada chart for the warranty data is provided in Table 11.3. The last two rows were combined, as specified in the example.
|
|
TTF
|
| TIS
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
Total
|
Sales Volume
|
|
|
| 12
|
3 |
0 |
3 |
3 |
4 |
2 |
1 |
5 |
4 |
2 |
3 |
3 |
45 |
2123
|
| 11
|
0 |
1 |
2 |
0 |
4 |
2 |
1 |
2 |
0 |
4 |
3 |
|
30 |
1853
|
| 10
|
1 |
3 |
2 |
2 |
3 |
4 |
3 |
5 |
4 |
8 |
|
|
45 |
2238
|
| 9
|
1 |
2 |
0 |
3 |
4 |
2 |
2 |
3 |
6 |
|
|
|
32 |
3052
|
| 8
|
2 |
3 |
2 |
6 |
2 |
1 |
6 |
4 |
|
|
|
|
34 |
2953
|
| 7
|
1 |
1 |
3 |
2 |
1 |
4 |
8 |
|
|
|
|
|
27 |
2788
|
| 6
|
1 |
0 |
1 |
0 |
1 |
2 |
|
|
|
|
|
|
11 |
2037
|
| 5
|
0 |
0 |
1 |
1 |
0 |
|
|
|
|
|
|
|
7 |
1863
|
| 4
|
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
6 |
1231
|
| 3
|
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
5 |
823
|
| 2
|
0 |
1 |
|
|
|
|
|
|
|
|
|
|
3 |
638
|
| 1
|
0 |
|
|
|
|
|
|
|
|
|
|
|
1 |
568
|
|
|
| Total
|
9 |
12 |
16 |
18 |
19 |
17 |
21 |
19 |
14 |
14 |
6 |
3 |
|
Result
The book first converted the data in the table above into the following format, as given in Table 11.4 in the book.
| TTF (Months)
|
Number of Failures
|
Number of Censored Units
|
| 1 |
9 |
568
|
| 2 |
12 |
637
|
| 3 |
16 |
821
|
| 4 |
18 |
1229
|
| 5 |
19 |
1861
|
| 6 |
17 |
2032
|
| 7 |
21 |
2768
|
| 8 |
19 |
2927
|
| 9 |
14 |
3029
|
| 10 |
14 |
2203
|
| 11 |
6 |
1834
|
| 12 |
3 |
2090
|
A lognormal distribution is used and the fitted model parameters are: Ln-Mean = 6.03 and Ln-Std = 1.63.
Results in Weibull++
In Weibull++, the data set is entered into a warranty folio, using the Nevada chart format. The following pictures show the sales and returns data.
The following picture shows the parameters of the lognormal distribution and its associated failure/suspension data. The results are the same as the results shown in the book.
The following picture shows the probability plot of the lognormal distribution.
